Bruhat Intervals in the Infinite Symmetric Group are Cohen-Macaulay
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909993471574016 |
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| author | Gallup, Nathaniel Gray, Leo |
| author_facet | Gallup, Nathaniel Gray, Leo |
| contents | We show that the (non-Noetherian) Stanley-Reisner ring of the order complex of certain intervals in the Bruhat order on the infinite symmetric group $S_\infty$ of all auto-bijections of $\mathbb{N}$ is Cohen-Macaulay in the sense of ideals and weak Bourbaki unmixed. This gives an infinite-dimensional version of results due to Edelman, Björner, and Kind and Kleinschmidt for finite symmetric groups $S_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12195 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bruhat Intervals in the Infinite Symmetric Group are Cohen-Macaulay Gallup, Nathaniel Gray, Leo Combinatorics Commutative Algebra 05E40, 13C14, 20B30 We show that the (non-Noetherian) Stanley-Reisner ring of the order complex of certain intervals in the Bruhat order on the infinite symmetric group $S_\infty$ of all auto-bijections of $\mathbb{N}$ is Cohen-Macaulay in the sense of ideals and weak Bourbaki unmixed. This gives an infinite-dimensional version of results due to Edelman, Björner, and Kind and Kleinschmidt for finite symmetric groups $S_n$. |
| title | Bruhat Intervals in the Infinite Symmetric Group are Cohen-Macaulay |
| topic | Combinatorics Commutative Algebra 05E40, 13C14, 20B30 |
| url | https://arxiv.org/abs/2601.12195 |